It's true verbal abuse counts as abuse, and can leave as lasting scars as physical abuse. But what counts as verbal abuse? Is it having a fight with your friend and saying something mean you regret later? Is it a guardian who loves her grandson dearly but tells him the truth--that with his miserable grades and seemingly lack of magical talent he isn't cut out to be an Auror like his heroic parents?
On the subject of Neville as a teacher, I think he would be a good teacher, and I can imagine him like Flitwick, in that he's nice and plans fun/educational lesson plans, but can tell someone to be quiet or pay attention if needs be.
Just for the record, Augusta Longbottom is the mother of Frank Longbottom, not Alice (whose maiden name I don't think we're ever told in the books).Even if his grandmother does burden him with excessive expectations -- and I can even imagine her being less than perfect, at times, perhaps losing her patience with a shy, uncertain child who is so not like her daughter -- that doesn't mean she verbally abuses him.